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      Symmetric coalescence of two hydraulic fractures

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      Proceedings of the National Academy of Sciences
      Proceedings of the National Academy of Sciences

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          Abstract

          <p id="d5586833e195">We present an experimental investigation on the coalescence of hydraulic fractures in a brittle solid. Using a dual-fracturing setup, we obtain high-resolution experimental measurements on the time evolution of the fracture profiles and internal velocity field before, during, and after fracture coalescence. These measurements show an intermediate time self-similar coalescence during the dynamic interaction of two fractures. The work probes the dynamic formation of a fracture network, which is crucial to the industrial practice of energy resource recovery, compensation grouting, and the reservoir integrity of many confined systems involving fluid injection. </p><p class="first" id="d5586833e198">The formation of a fracture network is a key process for many geophysical and industrial practices from energy resource recovery to induced seismic management. We focus on the initial stage of a fracture network formation using experiments on the symmetric coalescence of two equal coplanar, fluid-driven, penny-shaped fractures in a brittle elastic medium. Initially, the fractures propagate independently of each other. The fractures then begin to interact and coalesce, forming a bridge between them. Within an intermediate period after the initial contact, most of the fracture growth is localized along this bridge, perpendicular to the line connecting the injection sources. Using light attenuation and particle image velocimetry to measure both the fracture aperture and velocity field, we characterize the growth of this bridge. We model this behavior using a geometric volume conservation argument dependent on the symmetry of the interaction, with a 2D approximation for the bridge. We also verify experimentally the scaling for the bridge growth and the shape of the thickness profile along the bridge. The influence of elasticity and toughness of the solid, injection rate of the fluid, and initial location of the fractures are captured by our scaling. </p>

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          Fluid-mechanical models of crack propagation and their application to magma transport in dykes

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            Coalescence of spreading droplets on a wettable substrate.

            We investigate experimentally and theoretically the coalescence dynamics of two spreading droplets on a highly wettable substrate. Upon contact, surface tension drives a rapid motion perpendicular to the line of centers that joins the drops and lowers the total surface area. We find that the width of the growing meniscus bridge between the two droplets exhibits power-law behavior, growing at early times as t1/2. Moreover, the growth rate is highly sensitive to both the radii and heights of the droplets at contact, scaling as ho3/2/Ro. This size dependence differs significantly from the behavior of freely suspended droplets, in which the coalescence growth rate depends only weakly on the droplet size. We demonstrate that the scaling behavior is consistent with a model in which the growth of the meniscus bridge is governed by the viscously hindered flux from the droplets.
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              Self-Similar Solutions for Elastohydrodynamic Cavity Flow

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                Author and article information

                Journal
                Proceedings of the National Academy of Sciences
                Proc Natl Acad Sci USA
                Proceedings of the National Academy of Sciences
                0027-8424
                1091-6490
                October 09 2018
                October 09 2018
                October 09 2018
                September 25 2018
                : 115
                : 41
                : 10228-10232
                Article
                10.1073/pnas.1809233115
                6187166
                30254160
                9ba78da1-ea8b-4191-b3dd-fe56c0d96222
                © 2018

                Free to read

                http://www.pnas.org/site/misc/userlicense.xhtml

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